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- W2029930003 abstract "A 2-coloring ( G 1 , G 2 ) of a digraph is 2-primitive if there exist nonnegative integers h and k with h + k > 0 such that for each ordered pair ( u , v ) of vertices there exists an ( h , k ) -walk in ( G 1 , G 2 ) from u to v . The exponent of ( G 1 , G 2 ) is the minimum value of h + k taken over all such h and k . In this paper, we consider 2-colorings of strongly connected symmetric digraphs with loops, establish necessary and sufficient conditions for these to be 2-primitive and determine an upper bound on their exponents. We also characterize the 2-colored digraphs that attain the upper bound and the exponent set for this family of digraphs on n vertices." @default.
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- W2029930003 date "2008-04-01" @default.
- W2029930003 modified "2023-09-28" @default.
- W2029930003 title "Exponents of 2-coloring of symmetric digraphs" @default.
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- W2029930003 doi "https://doi.org/10.1016/j.laa.2007.09.027" @default.
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